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# br System description and data collection Fig shows

System description and data collection
Fig. 1 shows the arrangement of the system studied. It provided cooling Wang Resin to maintain thermal conditions in an institutional building. The locations of the measured variables (, and ) relating to temperature and flow rate are indicated in Fig. 1. The electric powers of all the system components were monitored via the central control and monitoring system (CCMS). All the measured variables and the on/off status of system components were logged by the CCMS at 15 min intervals. The monitoring period was from January to August. A total of 12,541 sets of operating conditions were gathered. Based on the measured and , the cooling capacity of the operating chillers was calculated by Eq. (1). The system COP given by Eq. (2) was the total cooling capacity of the operating chillers divided by the total electric power of the operating components. The heat rejection effectiveness of cooling towers depended on the wet bulb temperature (). Considering was not directly measured, it was calculated by the measured and RH based on the empirical equation given by Eq. (3) (Stull, 2011).
The conventional pair-up control was applied for chillers, primary loop chilled water pumps, condenser water pumps and cooling towers. The operating status under the conventional control was designated by 1111, 2222 or 3333, where the 1st digit represented the number of chillers operating, the 2nd digit for primary loop chilled water pumps, the 3rd digit for condenser water pumps and the 4th digit for cooling towers. The actual operation of the system had unconventional operating statuses with different numbers in the 4 digits. Such statuses occurred more frequently just before and after transitional statuses involving changes in the number of system components operating. The operation of cooling towers and their fan speed were controlled based on a set point of 29 °C for the cooling water entering the condensers. As the heat rejection effect depended on the interaction of the ambient wet bulb temperature and the load carried by the chillers, the number of cooling towers operating might be smaller or larger than that of chillers. This study focuses on the normal operating status with one operating chiller (1111), its unconventional statuses (1110 and 1112) with switching on or off one extra cooling tower, and the transitional statuses (1110→1111, 1111→1110, 1111→1112, 1112→1111). Other unconventional and transitional statuses were identified to be about 4.8% of the total operating conditions and analyzed elsewhere. Table 1 shows an excerpt of temporal operating data to be further compiled to develop Cox regression models.

Method of developing cox regression models
The measured variables influenced simultaneously the period from one operating status to another because the number of system components operating was controlled in response to the set point of and the calculated from the measured and . The period in which an operating status lasted for was referred to as the survival time which was addressed by survival analysis (Kleinbaum and Klein, 2012). Survival analysis is commonly used to address problems relating to biology, health and business-related disciplines but its application is rather limited for engineering problems. Hong et al. (2016) examined the use of survival analysis to overcome the challenge of modelling the occupancy behaviour for building energy simulation. Sancho-Tomása et al. (2017) modelled a survival function for the duration of an electrical appliance remaining in different energy states in order to improve a generalized model for predicting electricity demand from household appliances.
The Cox regression model given by Eq. (4) (Kleinbaum and Klein, 2012, Cox, 1972) is one of the survival analysis methods used to correlate a series of time-dependent risk factors (or covariates (t) i = 1 to p) with the hazard rate. The model estimates the instantaneous probability of observing a change given that a particular status has survived up to a specific time t. h0(t) is the baseline hazard and represents the hazard when all the covariates are zero. In this analysis, variables in columns 4 to 12 in Table 1 constituted (t) to (t), respectively. The data of the variables were standardized with a mean of zero and a standard deviation of one. The coefficients were determined by using the maximum partial likelihood method. Using standardized data, the dimensionless values of exp() were compared directly to examine their impacts on the hazard rate. The significant association of the variables was identified based on a threshold p-value of 0.05 or below.